Math: Algebra 2 Flashcards
(110 cards)
0
Q
Variation Functions:
How is a joint variation read?
A
y varies jointly as x and z
1
Q
Variation Functions:
How is an inverse variation read?
A
y varies inversely as x
2
Q
Variation Functions:
In a combined variation, quantities that vary directly appear in the ___ with _, and quantities that vary inversely appear in the _____
A
Numerator with k
Denominator
3
Q
Variation Functions:
A relationship between two variables x and y that can be written in the form y=kx
A
Direct variation
4
Q
Variation Functions:
A relationship that contains both direct and inverse variation.
A
Combined variation
5
Q
Variation Functions:
In all variation models, k is the __ of ____ and cannot equal _
A
Constant of variation
0
6
Q
Variation Functions:
How is a direct variation read?
A
y varies directly as x
7
Q
Variation Functions:
In direct variation, the __ of two quantities is constant. In inverse variation, the __ of the two quantities is constant
A
Ratio
Product
8
Q
Variation Functions:
A relationship among three variables that can be written in the form y=kxz
A
Joint variation
9
Q
Variation Functions:
A relationship between two variables x and y that can be written in the form y=k/x
A
Inverse variation
10
Q
Trigonometry:
For an angle theta in standard position, the __ __ is the positive acute angle formed by the terminal side of theta and the x-axis.
A
Reference angle
11
Q
Trigonometry:
The Greek letter _ is used to represent the measure of an acute angle in a right triangle
A
Theta
12
Q
Trigonometry:
The __ __ of the angle is the ray on the x-axis. The other ray is called the __ __ of the angle
A
Initial side
Terminal side
13
Q
Trigonometry:
If the terminal side is rotated counterclockwise, the angle of rotation is __. If the terminal side is rotated clockwise, the angle of rotation is __.
A
Positive
Negative
14
Q
Trigonometry:
A function whose rule is given by a trigonometric ratio
A
Trigonometric function
15
Q
Trigonometry:
Ratio of the hypotenuse over the adjacent leg
A
Secant (sec)
16
Q
Trigonometry:
An __ _ __ is formed by rotating the terminal side and keeping the initial side in place
A
Angle of rotation
17
Q
Trigonometry:
Ratio of the hypotenuse over the opposite leg
A
Cosecant (csc)
18
Q
Trigonometry:
The reciprocals of the sine, cosine, and tangent ratios are the trigonometric ratios __, __, & __
A
Cosecant
Secant
Cotangent
19
Q
Trigonometry:
An angle is in __ __ when its vertex is at the origin and one ray is on the positive x-axis
A
Standard position
20
Q
Trigonometry:
Ratio of the adjacent leg over the opposite leg
A
Cotangent (cot)
21
Q
Trigonometry:
When an object is above or below another object, you can find distances indirectly by using the __ _ __ or the __ _ __ between the objects
A
Angle of elevation
Angle of depression
22
Q
Trigonometry:
Ratio of the opposite leg over the adjacent leg
A
Tangent (tan)
23
Q
Trigonometry:
Ratio of opposite leg over the hypotenuse
A
Sine (sin)
24
Trigonometry:
| Ratio of adjacent leg over the hypotenuse
Cosine (cos)
25
Trigonometry:
| Angles in standard position with the same terminal side. Find by adding or subtracting integer multiples of __ degrees
Coterminal angles
| 360
26
Statistics:
| A continuous probability distribution for a random variable x.
Normal distribution
27
Statistics:
| A numerical description of a population characteristic
Parameter
28
Statistics:
| The distance from the mean a particular datum lies
Standard deviation
29
```
Statistics:
Determining if an event is unusual:
Less than _%, unusual
Over than _%, not unusual
* no specific % which determines if event is unusual or not
```
5%
| 5%
30
Statistics:
| Involves using a sample to draw conclusions about a population
Inferential
31
Statistics:
An investigation of one or more characteristics of a population. Most often carried out on people by asking them questions
Survey
32
Statistics:
Two cases to finding probabilities of independent events:
__:__ probabilities of each event
__:__ probabilities of each event
AND: multiply
OR: add
33
Statistics:
| The average of a set of data
Mean
34
Statistics:
Consists of numerical measurements or counts
Ex: number of students who eat breakfast
Quantitative Data
35
Statistics:
Which sampling method?:
Often leads to biased studies. Consists only of available members of the population
Convenience sample
36
Statistics:
The normal distribution with a mean of 0 and a standard deviation of 1 is called the _ _ _. The horizontal scale of the graph of the standard normal distribution corresponds to _-_
Standard normal distribution
| Z-scores
37
Statistics:
| What are the two types of data sets?
Population
| Sample
38
Statistics:
To find the z-score when given the area to the right of a z-score, use ___ function.
___(#)
invNorm()
| invNorm(1-area to right of z-score)
39
Statistics:
| Rule that will help see how valuable the standard deviation can be as a measure of variation
68-95-99.7 rule
40
Statistics:
| What are the two branches of statistics?
Descriptive
| Inferential
41
Statistics:
| To find the area to the left of the z score, use the __ function. ____(#,#).
normalcdf()
| normalcdf(-100000, given z-score)
42
Statistics:
| A numerical description of a sample characteristic
Statistic
43
Statistics:
| A count or measure of part of a population; often more practical than taking a census
Sampling
44
Statistics:
When choosing members of a sample, you should decide whether it is acceptable to have the same population member selected more than once. If acceptable, the sampling process is said to be __ ___. If it is not, the sampling process is said to be ___ __.
With replacement
| Without replacement
45
Statistics:
| Involves the organization, summarization, and display of data
Descriptive
46
Statistics:
Which sampling method?:
A sample in which each member of the population is assigned a number. The members of the population are ordered in some way , a starting # is randomly selected, and the n sample members are selected at regular intervals from the starting #
Systematic sample
47
Statistics:
| The science of collecting, organizing, analyzing, and interpreting data in order to make decisions
Statistics
48
Statistics:
Consists of attributes, labels, or non-numerical entries
Ex: what students eat for breakfast (eggs, toast, pancakes)
Qualitative Data
49
Statistics:
| A subset of a population
Sample
50
Statistics:
| What are 2 examples of independent events?
Flipping a coin
| Selecting marbles from a bag with replacement
51
Statistics:
| To find the area to the right of the z score, use the __ function. ____(#,#).
normalcdf()
| normalcdf(Given z-score, 100000)
52
```
Statistics:
Some cases where a normal model cannot be used:
1) data is __ either to the _ or _
2) data is __ (more than one _)
3) data is __ (no _)
```
Skewed, left or right
Bimodal, more than one mode
Consistent, no modes
53
Statistics:
Which sampling method?:
Sample in which every possible sample of the same size has the same chance of being selected
Simple random sample
54
Statistics:
| The graph of a normal distribution
Normal curve
55
Statistics:
| A treatment is applied to part of a population and responses are observed
Experiment
56
Statistics:
| Represents the number of standard deviations a given value falls from the mean
Standard score
| Z-score
57
Statistics:
| The collection of all outcomes, responses, measurements, or counts that are of interest
Population
58
Statistics:
Typically, any value that does not lie within _ standard deviations of the mean is considered ____ ____. This means that it is unusual that this event would occur.
2
| Statistically significant
59
Statistics:
| A count or measure of an entire population; provides complete information, but is often costly and difficult to perform
Census
60
Statistics:
| Consists of information coming from observations, counts, measurements, or responses
Data
| Singular: datum
61
Statistics:
If a z-score is negative, the corresponding x-value is ___ the mean. If a z-score is positive, the corresponding x-value is ___ the mean. If a z-score equals 0, the corresponding x-value is ___ the mean.
Below
Above
Equal to
62
Statistics:
Which sampling method?:
Ensures that each segment of the population is represented
Stratified sample
63
Statistics:
| Members of the population are divided into 2 or more subsets that share a similar characteristic
Strata
64
Statistics:
To find the area between 2 z-scores, use the __ function.
___(#,#)
normalcdf()
| normalcdf(first z-score, second z-score)
65
Statistics:
Properties of a normal distribution:
1) __, __, & ___ are equal
2) normal curve is __ __ and is ___ about the mean
3) total area under the normal curve is equal to _
4) the normal curve approaches but never touches the ____ as it extends farther and farther away from the mean
5) In the center of the curve, the graph curves ____ (__ __). The graph curves ___ (__ __) to the left of u-o and to the right of u+o.
```
Mean, median, mode
Bell-shaped, symmetric
1
X-axis
Downward, concave down
Upward, concave up
```
66
Statistics:
The use of a mathematical or physical model to reproduce the conditions of a situation or process. Allow you to study situations that are impractical or even dangerous to create in life. Often save time and money
Simulation
67
Statistics:
A researcher observes and measures the characteristics of interest of part of a population. The researcher does not influence the responses
Observational study
68
Statistics:
| How do you find the z-score?
(Value-mean)/ standard deviation
69
Statistics:
| Events that the occurrence of one event does not affect the probability of the other.
Independent events
70
Statistics:
Which sampling method?:
When population falls into naturally occurring subgroups, each having similar characteristics. Select all members in one or more(but not all) of the clusters
Cluster sample
71
Statistics:
Which sampling method?:
One in which every member of the population has an equal chance of being selected
Random sample
72
Statistics:
| The points at which the curve changes from curving up to curving down
Inflection points
73
Statistics:
| Each standard deviation equates to a z-score of _
1
74
Statistics:
| A basic tool in the study of inferential statistics
Probability
75
Statistics:
To find the z-score when given the area to the left of a z-score, use ___ function.
___(#)
invNorm()
| invNorm(area to left of z-score)
76
Statistics:
| Many real-life data sets have distributions that are approximately ____ and ____
Symmetric
| Bell-shaped
77
Statistics:
| Divide the population into groups of similar characteristics
Clusters
78
Functions:
| Vertical stretch and compression changes the _ value
Y
79
```
Functions:
Name the parent function:
f(x)= x
D: (- infinity, infinity)
R: ( -infinity, infinity)
Slope: 1
```
Linear
80
Functions:
Away from x-axis
(x,y) -> (x,ay); |a| > 1
Vertical stretch
81
Functions:
Toward the y-axis
(x,y) -> (bx,y); 0<|b|<1
Horizontal compression
82
```
Functions:
Name the parent function:
f(x)= x^3
D: (- infinity, infinity)
R: (- infinity, infinity)
```
Cubic
83
Functions:
Away from y-axis
(x,y) -> (bx,y); |b| > 1
Horizontal stretch
84
Functions:
| Horizontal stretch and compression changes the _ value
X
85
Functions:
f(x)= the square root of x
D: [0, infinity)
R: [0, infinity)
Square root
86
```
Functions:
Name the parent function:
f(x)= x^2
D: (- infinity, infinity)
R: [0, infinity)
```
Quadratic
87
Functions:
Toward the x-axis
(x,y) -> (x,ay); 0<|a|<1
Vertical compression
88
Matrices:
| rectangular arrangement of numbers
Matrix
89
Matrices:
| The product of 2 or more matrices is called a _____ _____
Matrix product
90
Matrices:
| A message written according to a secret code
Cryptogram
91
Matrices:
The _____ _____ matrix is a square matrix that has all the entries along the main diagonal equal to 1 & all of the other entries equal to 0
Multiplicative identity
92
Matrices:
| Two matrices are ____ if they have the same dimensions and their corresponding entries are equal
Equal
93
Matrices:
| In matrix algebra, a real number is called a _____
Scalar
94
Matrices:
| Each number/term in a matrix is called an ____ or an _____
Entry
| Element
95
Matrices:
| A ____ matrix contains only one column
Column
96
Matrices:
| A network where arrows show direction of travel between vertices
Directed network
97
Matrices:
| 2 square matrices are ____ of each other if their product (in both orders) is the identity matrix
Inverses
98
Matrices:
| The goal of row reduction is to transform the augmented matrix to ____ __-____ ___
Reduced row-echelon form
99
Matrices:
| The process of performing elementary row operations on an augmented matrix to solve the system
Row reduction
100
Matrices:
| A ___ matrix contains only one row
Row
101
Matrices:
| Matrices can only be added/subtracted if they have the same ______
Dimensions
102
Matrices:
| A finite set of connected points called vertices
Network
103
Matrices:
| The ___ diagonal of a square matrix is the diagonal from the upper left corner to the lower right corner
Main
104
Matrices:
| What is the equation of finding the inverse of a 2x2 matrix?
1/det(A)* [d -b]
| [-c a]
105
Matrices:
| Associated with each square matrix is a real # called a
Determinant
106
Matrices:
| A ____ matrix has the same number of rows & columns
Square
107
Matrices:
| You can use determinants to solve a system of linear equations using a method called
Cramer's rule
108
Matrices:
| Size of a matrix
Dimensions
109
Matrices:
| Location of a # in a matrix
Address
